Crystal Packing Factor-guided Design of Stress-resistant Alloying-type Anodes for Durable Sodium-ion Storage

Abstract

Alloying-type anodes hold promise for sodium-ion batteries (SIBs) due to their high theoretical capacities, yet they suffer from severe capacity fading caused by large volume expansion during sodiation. Identifying a universal structural descriptor that links lattice chemistry with stress resistance and ion transport is therefore critical. Here, we introduce the crystal packing factor (PF) as a predictive metric and validate its effectiveness in layered bismuth compounds (BiOCl, Bi₂O₂S, and Bi₂O₂NCN) spanning a broad PF range. Bi₂O₂NCN, characterized by an atomically sparse and electronically conjugated [Bi₂O₂]²⁺-NCN²⁻ layered framework with the lowest PF (0.613), markedly outperforms Bi₂O₂S (0.694) and BiOCl (0.763). Its open framework provides abundant interlayer free volume and weak steric constraints, thereby buffering mechanical strain and accelerating Na⁺ diffusion. First-principles calculations corroborate that Bi₂O₂NCN shows suppressed stress accumulation and a lower migration barrier of 0.18 eV compared to Bi₂O₂S and BiOCl. Experimentally, Bi₂O₂NCN delivers a high capacity of 486 mA·h·g⁻¹ at 0.3 C (1 C=656 mA·g⁻¹) and maintains 230 mA·h·g⁻¹ after 6600 cycles at 15 C with 93% capacity retention. Multimodal structural characterizations further confirm a reversible conversion-alloying mechanism. These findings establish the crystal PF as a generalizable guideline for designing stress-resistant alloying-type anodes, offering a powerful pathway toward durable, high-performance SIBs.

Keywords

Crystal packing factor / Stress resistance / Bismuth oxide carbodiimide / Anode material / Sodium ion battery

References

[1] DunnB, KamathH, TarasconJ-MScience, 2011, 334928.

[2] SunS, WangK, HongZ, ZhiM, ZhangK, XuJNano-Micro Lett., 2023, 1635.

[3] UsiskinR, LuY, PopovicJ, LawM, BalayaP, HuY-S, MaierJNat. Rev. Mater., 2021, 61020.

[4] RudolaA, SayersR, WrightC J, BarkerJNat. Energy, 2023, 8215.

[5] HwangJ-Y, MyungS-T, SunY-KChem. Soc. Rev., 2017, 463529.

[6] DuffnerF, KronemeyerN, TuebkeJ, LekerJ, WinterM, SchmuchRNat. Energy, 2021, 6123.

[7] Li Q., Zhang H., Xu J., Chin. Sci. Bull., 2025, https://doi.org/10.1360/CSB-2025-0404.

[8] QianH, LiuY, ChenH, FengK, JiaK, PanK, WangG, HuangT, PangX, ZhangQEnergy Storage Mater., 2023, 58232.

[9] WangA, HongW, YangL, TianY, QiuX, ZouG, HouH, JiXSmall, 2020, 162004022.

[10] LvZ, XuH, XuW, PengB, ZhaoC, XieM, LvX, GaoY, HuK, FangY, DongW, HuangFAdv. Energy Mater., 2023, 132300790.

[11] LvZ, PengB, LvX, GaoY, HuK, DongW, ZhengG, HuangFAdv. Funct. Mater., 2023, 332214370.

[12] WuZ, LiangG, WuJ, PangW K, YangF, ChenL, JohannessenB, GuoZAdv. Energy Mater., 2021, 112100185.

[13] SunJ, TuW, ChenC, PlewaA, YeH, Sam OhJ A, HeL, WuT, ZengK, LuLChem. Mater., 2019, 317311.

[14] DuttaP K, MyungY, VenkiteswaranR K, MehdiL, BrowningN, BanerjeeP, MitraSThe Journal of Physical Chemistry C, 2019, 12311500.

[15] HaoG, ZhangC, ChenZ, XuYAdv. Funct. Mater., 2022, 322201352.

[16] FangS-J, DuP, ZhangJ-F, WangC-H, XiaoZ-M, ZhangB, CaoL, FanX-M, OuXRare Met., 2022, 412567.

[17] Mo F., Liu Z., Li H., Adv. Funct. Mater., 2025, n/a, e13591.

[18] ZhangK-L, LiuC-M, HuangF-Q, ZhengC, WangW-DAppl. Catal. B, 2006, 68125.

[19] DongW, HuangFeScience, 2024, 4100158.

[20] ShannonR DActa Crystallographica Section A, 1976, 32751.

[21] LinX, HuangF, WangW, WangY, XiaY, ShiJAppl. Catal. A, 2006, 313218.

[22] ZhengL, XuY, JinD, XieYChem. Mater., 2009, 215681.

[23] KongS, LvX, WangX, LiuZ, LiZ, JiaB, SunD, YangC, LiuL, GuanA, WangJ, ZhengG, HuangFNat. Catal., 2023, 66.

[24] Liao H., Tang Y., Ma W., Liu Y., Dong Y., Huang F., Nat. Energy, 2025, https://doi.org/10.1038/s41560-025-01831-8.

[25] LvC, LinC, ZhaoX SeScience, 2023, 3100179.

[26] DongW, LiuZ, XieM, ChenY, MaW, LiangS, BaiY, HuangFAdv. Mater., 2024, 362311424.

[27] LvZ, DongW, JiaB, ZhangS, XieM, ZhaoW, HuangFChem. Eur. J., 2021, 272717.

[28] LiaoH, CaiM, MaW, CaoY, ZhaoS, DongY, HuangFAdv. Mater., 2024, 362402739.

[29] HuK, ChenW, PanY, LiS, LvZ, HeY, ZhengC, HuangF, DongWNano Lett., 2025, 251823.

[30] JiaB, ChenZ, LiC, LiZ, ZhouX, WangT, YangW, SunL, ZhangBJ. Am. Chem. Soc., 2023, 14514101.

[31] SougratiM T, ArayamparambilJ J, LiuX, MannM, SlabonA, StievanoL, DronskowskiRDalton Trans., 2018, 4710827.

[32] WangJ J, BuiH T D, WangX, LvZ, HuH, KongS, WangZ, LiuL, ChenW, BiH, YangM, BrinckT, WangJ, HuangFJ. Am. Chem. Soc., 2025, 1478012.

[33] JiaB, SunD, ZhaoW, HuangFJ. Energy Chem., 2021, 61347.

[34] LiQ, GaoB, ZhengX, LiuX, CuiX, ChengM, YanX, LiuH, YangH, KongW, WangZ, WuW, XuQApplied Catalysis B: Environment and Energy, 2025, 368125133.

[35] LvZ, ZhaoC, XieM, CaiM, PengB, RenD, FangY, DongW, ZhaoW, LinT, LvX, ZhengG, HuangFAdv. Mater., 2024, 362309637.

[36] LiuC, ZhangC, FuH, NanX, CaoGAdv. Energy Mater., 2017, 71601127.

[37] WuZ-J, ZhaoE-J, XiangH-P, HaoX-F, LiuX-J, MengJPhysical Review B, 2007, 76054115.

[38] FengY, XuM, HeT, ChenB, GuF, ZuL, MengR, YangJAdv. Mater., 2021, 332007262.

[39] ChenZ, XiaoY, QiaoX, OuH, LeeC-F, WangH-T, ShaoY-C, HanLProceedings of the National Academy of Sciences, 2025, 122e2420922122.

[40] MüllerR J, LanJ, LienauK, MoréR, TrianaC A, LannuzziM, PatzkeG RDalton Trans., 2018, 4710759.

[41] YueK, QinY, HuangH, LvZ, CaiM, SuY, HuangF, YanYNat. Commun., 2024, 157820.

[42] ZhuK, JiaB, ChenZ, HuZ, SunL, WangT, ZhangBAngew. Chem. Int. Ed., 2025, 64e202507422.

[43] WangJ, BuiH T D, HuH, KongS, WangX, ZhuH, MaJ, XuJ, LiuY, LiuL, ChenW, BiH, YangM, HuangF, BrinckT, WangJAdv. Mater., 2025, 372418451.

[44] CorkettA J, ChenZ, BogdanovskiD, SlabonA, DronskowskiRInorg. Chem., 2019, 586467.

[45] JiaB, ZhaoW, SunD, FanL, YaoH, LuP, XuF, HuangFChem. Mater., 2019, 319532.

[46] LongH, WangJ, ZhaoS, ZouB, YanL, HuangQ, ZhaoYAngew. Chem. Int. Ed., 2024, 63e202406513.

[47] LuZ, YuH, WeiY, CaoC, LiangR, CaiG, JinS, JinH, NiY, LinY, JiHJ. Am. Chem. Soc., 2025, 14728714.

RIGHTS & PERMISSIONS

Jilin University, The Editorial Department of Chemical Research in Chinese Universities and Springer-Verlag GmbH